I circled what I believe to be the chiral centers and I added the locants for the longest carbon chain. One of the chiral centers is in a side chain, so that carbon doesn't have a locant. How should its absolute configuration be included into the IUPAC name?
You have correctly ideentified and numbered the parent structure (the longest chain), which is undec-3-yne.
Including the substituent groups, the complete name is 10-bromo-5-(butan-2-yl)-2-methylundec-3-yne.
Note that names for simple substituent groups derived from acyclic hydrocarbons with the free valence not at the end of the chain are generically called ‘alkanyl’. A low locant is assigned to the free valence (i.e. the suffix ‘yl’) in accordance with the numbering of the chain. In this case, butan-2-yl is such a substituent group.
Also note that the locant ‘2’ in butan-2-yl refers to a different structural element compared to the other locants in 10-bromo-5-(butan-2-yl)-2-methylundec-3-yne. Therefore, parentheses are used around the substituent prefix to separate the locants.
If you need to indicate the stereochemical configuration, the same numbering and separation of locants is used, for example: (5R,10R)-10-bromo-5-[(2S)-butan-2-yl]-2-methylundec-3-yne.